1. Technical Field
The present invention relates to a thickness vibration mode piezoelectric vibrator, and in particular to a piezoelectric vibrating element (a vibrating element), a piezoelectric vibrator (a vibrator), a piezoelectric oscillator (an oscillator), and an electronic device each having a so-called mesa structure.
2. Related Art
A quartz crystal vibrating element using an AT-cut quartz crystal vibrating element has the vibration mode of thickness-shear vibration, and has frequency temperature characteristics showing an excellent cubic curve, and is therefore used in a number of fronts such as electronic equipment.
JP-A-58-047316 (Document 1) discloses a piezoelectric vibrator (an AT-cut quartz crystal vibrator) of a so-called mesa structure having the same level of energy confinement effect as that of the bevel structure or the convex structure.
It is known that, in the thickness-shear vibrator having a small length-to-thickness ratio (a ratio of the length of the side to the thickness), the contour vibration (e.g., flexural vibration) due to the contour dimension of the piezoelectric substrate is combined with the principal vibration to thereby degrade the characteristics of the principal vibration unless the length-to-thickness ratio is set appropriately.
JP-UM-A-06-052230 (Document 2) discloses the fact that, in view of the problem that an extraction electrode (a lead electrode) extending from each of excitation electrodes is broken if a sidewall in a boundary section between a mesa portion and a thin-wall portion is at an angle of 90° with a principal surface in an AT-cut quartz crystal vibrator formed to have a mesa structure, the broken line of the lead electrode can be prevented by forming the sidewall of the boundary section to be tilted or to have a curved surface. Further, it is also disclosed that by setting the roughness of a surface of the vibrating portion to a surface roughness as low as 0.2 micron in average roughness, the CI value is lowered, and thus the secondary vibration is suppressed.
Further, JP-A-2001-230655 (Document 3) discloses a quartz crystal vibrator having combination of the thickness-shear vibration and the flexural vibration suppressed by forming the AT-cut quartz crystal vibrator to have the mesa structure and tilting the sidewall of the mesa portion 63°, 35°.
Japanese Patent No. 4341583 (Document 4) discloses the fact that assuming that the frequency of a quartz crystal vibrating element is “f,” the length of a long side (X axis) of a quartz crystal substrate is “X,” the thickness of a mesa portion (the vibrating portion) is “t,” the length of a long side of the mesa portion is “Mx,” the length of a long side of each of excitation electrodes is “Ex,” and the wavelength of a flexural vibration caused in the long-side direction of the quartz crystal substrate is “λ,” by setting the parameters f, X, Mx, and Ex so as to fulfill the following four formulas, the thickness-shear vibration and the flexural vibration can be prevented from being combined.λ/2=(1.332/f)−0.0024  (1)(Mx−Ex)/2=λ/2  (2)Mx/2=(n/2+1/4)λ (where n is an integer)  (3)λ≧20t  (4)
JP-A-2008-263387 (Document 5) discloses the fact that assuming that the dimension of the long side of a piezoelectric substrate is “x,” and the thickness dimension of a mesa portion (a vibrating portion) is “t,” by setting the length-to-thickness ratio so that the height (a digging amount of a step section) y of a mesa portion of the piezoelectric substrate having a mesa structure fulfills the following formula with reference to the substrate thickness t, an unwanted mode can be suppressed.y=−0.89×(x/t)+34±3(%)
JP-A-2010-062723 (Document 6) discloses the fact that assuming that the length of a short side of a piezoelectric substrate having a mesa structure is “Z,” the thickness of a mesa portion (a vibrating portion) is “t,” and the electrode dimension in a short side direction of the mesa portion is “Mz,” by setting these parameters to fulfill the following relationship, the unwanted mode can be suppressed.15.68≦Z/t≦15.84, and 0.77≦Mz/Z≦0.82
However, in the piezoelectric vibrator having smaller length-to-thickness ratio, there is a problem that the vibratory displacement is not sufficiently attenuated in an end portion of the X axis to thereby excite the unwanted flexural mode in the end surface, which is combined with the principal vibration.
JP-A-02-057009 (Document 7) discloses the fact that by making the mesa structure have multiple steps, it becomes possible to more completely confine the vibration energy of the principal vibration.
Japanese Patent No. 3731348 (Document 8) discloses the fact that by constituting a piezoelectric substrate having a convex cross-sectional shape along the envelope curve of a supposed convex shape so as to have a staircase shape, it can approximately be replaced, and further, if the side surface having the staircase shape is replaced with a slope, the degree of approximation is increased.
JP-A-2008-236439 (Document 9) and JP-A-2010-109527 (Document 10) disclose the fact that by making a mesa portion of a piezoelectric substrate having a mesa structure have multiple steps, it is possible to enhance the energy confinement effect of a principal vibration to thereby suppress the unwanted mode.
JP-A-2009-130543 (Document 11) discloses a mesa vibration device using a step portion of a mesa structure as a flow stopper of an electrically-conductive adhesive to thereby achieve inflow prevention of the adhesive to the mesa portion. As described above, Documents 7 through 11 disclose the fact that it is effective for suppressing the combination of the principal vibration and the flexural vibration to making the mesa structure of the piezoelectric substrate be the multistage mesa structure to thereby deepen the energy confinement.
In the recent small-sized piezoelectric vibrator, when housing the piezoelectric vibrating element having a mesa structure inside a surface mount package and then sealing the package with a lid member, the piezoelectric vibrating element is supported by a so-called cantilever method in which one edge portion of the piezoelectric vibrating element is adhesively fixed to an element mounting pad in the package using an electrically-conductive adhesive, and the other edge portion opposed to the one edge portion is set to a free end. However, since the package shape is small, there is a problem that a necessary amount of electrically-conductive adhesive fails to be provided to thereby easily degrade the adhesion force, and thus the principal surface of the piezoelectric vibrating element is tilted, and the excitation electrodes have contact with an inner bottom of the package to thereby cause a malfunction.
Japanese Patent No. 4075893 (Document 12) discloses a manufacturing method of an AT-cut quartz crystal vibrator having a multistage mesa structure using a laser.
Further, JP-A-2004-200777 (Document 13) discloses a piezoelectric vibrating element having a structure in which a vibrating portion has a mesa structure, one edge of a thin-wall portion across the mesa portion is formed as a thick-wall projection section, and at least apart of the other edge opposed thereto is formed as a thick-wall projection section. When mounting the thick-wall projection section on the other edge on the element mounting pad using the electrically-conductive adhesive, the thick-wall projection section provided to the one edge stays in a space of a cavity of the package, has contact with an inner bottom of the package, or has contact with a lid member. It is disclosed that, because of the configuration described above, since there is no possibility for excitation electrodes provided to the mesa portion to have contact with the inner bottom of the package or the lid member, and the vibration of the piezoelectric vibrating element is not hindered, stable characteristics can be obtained.
However, the vibratory displacement energy of the quartz crystal vibrating element takes the maximum value at the center of each of the excitation electrodes, and is attenuated as the position moves away from the center toward the periphery. When plotting the parts having the same value of the vibratory displacement energy, there is drawn a plurality of ellipses having substantially similar shapes centered on the center thereof called isodynamic lines. In the quartz crystal vibrating element of Document 13, there is a problem that although the thick-wall projection section provided to the one edge thereof in the longitudinal direction (the X-axis direction) has the function of preventing the excitation electrodes and the package from having contact with each other, some of the vibratory displacement energy of the quartz crystal vibrating element is lost due to the interference with the thick-wall projection section provided to the one edge. The smaller the quartz crystal vibrating element is made, the larger the influence rate of the loss becomes, and there is a problem that it is difficult to stabilize the electrical characteristics of the quartz crystal vibrator.
JP-A-2010-114620 (Document 14) discloses a piezoelectric vibrating element having a mesa structure having a projection section at one end portion opposed to the other end portion at which the piezoelectric vibrating element is cantilevered. The projection section is disposed in at least one place in the corner portions excepting the central portion in the width direction of the other end portion. The projection section is disposed in the corner portion furthest from the center of the piezoelectric vibrating element having the mesa structure to thereby make the projection section have contact with the housing member. It is disclosed that according to this configuration, a piezoelectric vibrator with stable electrical characteristics can be obtained even if the piezoelectric vibrating element is miniaturized.
However, in the thickness-shear vibrating element using a quartz crystal substrate having a multistage mesa structure with the long-side direction parallel to the X axis (the electrical axis as one of the crystal axes of the quartz crystal), there is a problem that in the condition in which the X length-to-thickness ratio (the ratio X/t of the long-side dimension X to the thickness t) is low, for example, the ratio X/t is equal to or lower than 17, there occurs the combination of the thickness-shear vibration and contour vibration (e.g., a flexural vibration) in a direction parallel to a Z′ axis (an axis obtained by rotating an optical axis as one of the crystal axes of the quartz crystal as much as a predetermined angle taking the X axis as the central axis).
Further, the pad provided to an end portion of the quartz crystal vibrating element having the multistage mesa structure is mounted on the element mounting pad formed on the inner bottom of the package, and is then fixed with an electrically-conductive adhesive in a conductive manner to thereby constitute a quartz crystal vibrator. On this occasion, there is a problem that it is difficult to keep the both principal surfaces of the quartz crystal vibrating element and the bottom of the package parallel to each other due to the amount and the viscosity of the electrically-conductive adhesive applied to the element mounting pad, and the excitation electrodes of the quartz crystal vibrating element have contact with the bottom of the package or the lid member for seal to thereby deteriorate the electrical characteristics of the quartz crystal vibrator.